By selling an item for ₹75, the shopkeeper earns the percent profit equal to cost price of the item. Find the cost price of the item.
50
Let the cost price be x
Profit on the item is 75−x
Profit % = S.P−C.PC.P×100
=75−xx×100
Given that the profit percentage is equal to the cost price.
⇒75−xx×100=x
⇒x2=7500−100x
⇒x2−7500+100x=0
⇒x2+150x−50x−7500=0
⇒x(x+150)−50(x+150)=0
⇒(x+150)(x−50)=0
⇒x=−150 or 50
Cost price of an item cannot be negative. So, the cost price is ₹50